Galois structure of de Rham cohomology
Gauss–Manin connections for -adic families of nearly overconvergent modular forms
We interpolate the Gauss–Manin connection in -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type to the space of nearly overconvergent modular forms of type with -adic weight shifted by . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.
Géométrie rigide et cohomologie des variétés algébriques de caractéristique p